1. Three vectors are added together. The magnitude of the resultant vector may b

Question

1. Three vectors are added together. The magnitude of the resultant vector may be
a. equal to the sum of the magnitudes.
b. greater than the sum of the magnitudes.
c. less than the sum of the magnitudes.
d. either a or b, depending on the circumstances.
e. either a or c, depending on the circumstances.
f. any of a, b, or c, depending on the circumstances.

2. Which of the operations below is not mathematically allowed?
a. Addition of a vector and a scalar.
b. Multiplication of a vector and a scalar.
c. Addition of perpendicular vectors.
d. Dividing of a vector by a scalar.
e. More than one of the above is not allowed.

3. In a two dimensional rectangular coordinate system, if the x-component of a vector and
the angle between the vector and the x-axis are known, then the total magnitude of the
vector can be calculated by which of the following operations?
a. Dividing the x-component by the cosine of the angle.
b. Multiplying the x-component by the cosine of the angle.
c. Dividing the x-component by the sine of the angle.
d. Multiplying the x-component by the sine of the angle.
e. Dividing the x-component by the tangent of the angle.
f. Multiplying the x-component by the tangent of the angle.

4. How many scalar quantities are in the following list: velocity, speed, acceleration,
temperature, mass.
a. One
b. Two
c. Three
d. Four

Explanation / Answer

1. E. The resultant will either have all arrow pointing in the same direction, for which the answer is equal to, or one or more of the vectors will have an angle, which means the resultant is less than the sum of the magnitudes ( to help explain this, think of a right triangle - the hypotenuse will never be greater than the addition of the 2 legs. A 3-4-5 triangle has a hypotenuse of 5, which is less than 3+4=7 ).

2. A. Addition requires like terms, while multiplication does not. You cannot add Force to distance, but you CAN multiply force times distance ( equals energy )

3. Well, since we know the x component, and the angle between the vector and the x-axis, then lets use cos:

cos = adjacent/hypotenuse

cos = x component / vector magnitude

cross multiply and you get vecror magnitude = x component / cos

Therefore, the answer is A.

4. speed, temperature and mass are scalar. velocity and acceleration are vecotrs. Therefore, there are 3 scalars. So the answer is C.

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